When running a virtualized operating system on my Mac, is it important to have anti virus software?

Just curious if it is important to have anti virus for a virtualized operating system I got to thinking, that operating system is actively connecting to the Internet, so I thought maybe it had vulnerabilities.

If you are virtualizing a version of Windows, I would recommend you do use anti-virus software. Although Windows is running in a VM, it still is Windows and is vulnerable to viruses. A good choice of anti-virus software for Windows is Microsoft Security Essentials, which is free from Microsoft. (Note that: "Your PC must run genuine Windows to install Microsoft Security Essentials.")

If you are virtualizing a Linux distro, there is malware for Linux, so I would recommend anti-virus as well. There are several listed on the Linux malware Wikipedia page, including Avast! (Free) and AVG (Free).